{"pk":65004,"title":"Piecewise-linear promotion and RSK in rectangles and moon polyominoes","subtitle":null,"abstract":"We study piecewise-linear and birational lifts of Schützenberger promotion, evacuation, and the RSK correspondence defined in terms of toggles. Using this perspective, we prove that certain chain statistics in rectangles shift predictably under the action of these maps. We then use this to construct piecewise-linear and birational versions of Rubey's bijections between fillings of equivalent moon polyominoes that preserve these chain statistics, and we show that these maps form a commuting diagram. We also discuss how these results imply Ehrhart equivalence and Ehrhart quasi-polynomial period collapse of certain analogues of chain polytopes for moon polyominoes.\n \nMathematics Subject Classifications: 05E18, 05A05, 05A19, 52B05\n \nKeywords: Birational rowmotion, Robinson-Schensted-Knuth correspondence, moon polyominoes, period collapse","language":"en","license":{"name":"Creative Commons Attribution 4.0","short_name":"CC BY 4.0","text":"Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.\n\nNo additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.","url":"https://creativecommons.org/licenses/by/4.0"},"keywords":[{"word":"Birational rowmotion"},{"word":"Robinson-Schensted-Knuth correspondence"},{"word":"moon polyominoes"},{"word":"period collapse"}],"section":"Research Articles","is_remote":true,"remote_url":"https://escholarship.org/uc/item/82m6c1mt","frozenauthors":[{"first_name":"Joseph","middle_name":"","last_name":"Johnson","name_suffix":"","institution":"Institutionen för Matematik, KTH Royal Institute of Technology, Stockholm, Sweden","department":""},{"first_name":"Ricky","middle_name":"Ini","last_name":"Liu","name_suffix":"","institution":"Department of Mathematics, University of Washington, Seattle, WA, U.S.A.","department":""}],"date_submitted":"2025-09-12T13:58:21+02:00","date_accepted":"2025-09-12T13:58:21+02:00","date_published":"2025-09-15T09:00:00+02:00","render_galley":null,"galleys":[{"label":"","type":"pdf","path":"https://journalpub.escholarship.org/combinatorial_theory/article/65004/galley/49814/download/"}]}